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| Case 1: txy > 0 and sx > sy |
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The principal axes are counterclockwise to the current axes (because txy > 0) and no more than 45º away (because sx > sy).
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| Case 2: txy < 0 and sx > sy |
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The principal axes are clockwise to the current axes (because txy < 0) and no more than 45º away (because sx > sy).
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| Case 3: txy > 0 and sx < sy |
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The principal axes are counterclockwise to the current axes (because txy > 0) and between 45º and 90º away (because sx < sy).
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| Case 4: txy < 0 and sx < sy |
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The principal axes are clockwise to the current axes (because txy < 0) and between 45º and 90º away (because sx < sy).
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| Case 5: txy = 0 and sx > sy |
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The principal axes are aligned with the current axes (because sx > sy and txy = 0).
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| Case 6: txy = 0 and sx < sy |
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The principal axes are exactly 90° from the current axes (because sx < sy and txy = 0).
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